»ã±¨±êÌâ (Title)£ºWave Solutions in Reaction Diffusion Models of Brain Cancer Growth and Implications£¨ÄÔÖ×ÁöÊýѧģÐÍ·ÖÎö¼°ÀûÓã©
»ã±¨ÈË (Speaker)£º¿öÑô ½ÌÊÚ£¨ÃÀ¹úÑÇÀûÉ£ÄÇÖÝÁ¢´óѧ£©
»ã±¨¹¦·ò (Time)£º2025Äê5ÔÂ28ÈÕ(ÖÜÈý) 15:00-17:00
»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303
Ô¼ÇëÈË(Inviter)£ºÀƷ¡¢²ÌÃô
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»ã±¨ÌáÒª£ºGlioblastoma multiforme (GBM) is an aggressive primary brain cancer with a grim prognosis. Its morphology is heterogeneous, but prototypically consists of an inner, largely necrotic core surrounded by an outer, contrast-enhancing rim, and often extensive tumor-associated edema beyond. This structure is usually demonstrated by magnetic resonance imaging (MRI). To help relate the three highly idealized components of GBMs (i.e., necrotic core, enhancing rim, and maximum edema extent) to the underlying growth ¡°laws,¡± a mathematical model of GBM growth with explicit motility, birth, and death processes are proposed. This model generates a traveling-wave solution that mimics tumor progression. Such wave profile can be compared with MRI data to approximate patient specific model parameters. We use several test cases of MRI data of GBM patients to yield personalized parameterizations of the model, and the biological and clinical implications are discussed. In general,
existing models of GBM growth often include two separate equations to model proliferation or migration processes. Motivated by an in vitro experiment data set of GBM growth, we formulate, validate, simulate, study and compare two plausible models of GBM growth. We propose first a single equation which uses density dependent diffusion to capture the behavior of both proliferation and migration. We analyze the model to determine the existence of traveling wave solutions. To prove the viability of the density-dependent diffusion function chosen, we compare our model with the in vitro experimental data. Our second model is builti on the Go or Grow hypothesis since glioma cells tend to exhibit a dichotomous behavior: a cell either primarily proliferates or primarily migrates.
